8.4 Bandwidth vs. Frequency - Subsampling Concepts

Hello, and welcome to TI Precision Labs TIPL 4700, bandwidth versus frequency concepts. In this video, we will discuss the concept of Nyquist frequency, aliasing, undersampling, and input bandwidth.
Sampling an analog signal, we will start with the question why do we need to sample analog signals and convert them to digital domain?
Analog signals are converted to digital domain because they can be easily processed and saved in digital form. To better understand sampling, let's start with a basic plot diagram.
Shown in the plot diagram is an analog signal with frequency Fin applied to the input of the ADC and converted to digital data at the sampling frequency, Fs. Sampling frequency of an ADC is how often a sample from analog signal is captured and converted into digital data by the ADC.
Now we know that analog signal need to be converted into digital domain in order for processing and data storage. The next question that comes to mind is how often the analog signal should be sampled.
There is a theorem called Nyquist-Shannon sampling theorem that tells us how often an analog signal should be sampled in order to preserve all the information contained in the signal. This theorem states that sampling frequency should be more than twice of the highest frequency contained in the analog signal which needs to be sampled. Or in other words, Fin should always be less than Fs over 2.
The figure on the screen shows an analog signal sampled five times in one period. The sampling is shown with red markers. Sampling frequency is five times the input frequency of the signal. The Nyquist criteria of Fin over Fs over 2 is met, and we should be able to extract all the information contained in analog signal. Sampling a signal higher than Nyquist frequency is called oversampling.
What is aliasing, or under sampling? The term aliasing means false name. Aliasing occurs when Nyquist criteria is not met and Fin is greater than Fs over 2, and it becomes impossible to distinguish a low frequency signal from a high frequency signal. As shown in the figure, the frequency of red signal is 10 over nine times Fs, and frequency of blue signal is 1 over 9 times Fs. Both signals are sampled at sampling frequency Fs.
After sampling, it is impossible to distinguish red signal from blue signal. Both signals look like 1 over 9 times Fs to the ADC. Thus, one might say that that signal has been aliased down, or undersampled to the frequency of the blue signal.
Now let's look at oversampling and undersampling in frequency domain. In both cases, the same signal is sampled at different sampling frequencies. When the signal is oversampled, that is, the input frequency of the signal is less than half the sampling rate, as stated by Nyquist's theorem, the ADC outputs correct representation of the input signal, whereas when a signal is undersampled, that is, the input frequency of the signal is more than half the sample rate, the input signal is aliased down to a lower frequency, and we do not get correct representation of the input signal.
Nyquist zones. When talking about high speed data converters, often the term Nyquist zone is used. The frequency spectrum of an ADC is divided into different zones, based on the sampling frequency. Each Nyquist zone has bandwidth of half the data converter sampling rate. As shown in the figure, first Nyquist zone is from DC to Fs over 2, and second Nyquist zone is from Fs over 2 to Fs, and so on.
Practical aliasing example. At first, aliasing may appear to be undesirable. However, it can be very useful. The most useful property is mixing a higher frequency signal to a lower frequency. This can translate into cost saving, power saving, or board space saving by removing the need of an additional mixer stage. To achieve these desirable savings, care must be taken in frequency planning and ADC selection.
In previous, examples we used single frequency signals. In reality, single frequency signals rarely exist in a system. Most systems use wideband signals. A wideband signal can simply be defined as many frequencies within a specified bandwidth.
There are two things that should be kept in mind when frequency planning for using aliasing. First, the input signals bandwidth should be less than half the sampling rate. And secondly, the signal should completely fit in single Nyquist zone. That is, signals should not overlap two Nyquist zones.
We learned when a signal is in undersampled, it will alias down into first Nyquist zone. In order to understand and visualize sampling and aliasing, we use fan folding technique.
We assume a sheet that is transparent and folds every one half sample rate. Like a folding fan the size of each fold is equal to a Nyquist zone. To visualize the effect of sampling, we fold the paper and observe all the signals in different Nyquist zone have been superimposed to first Nyquist zone, and it is impossible to tell them apart.
To better understand aliasing and frequency folding, a signal is swept with increasing frequency to different Nyquist zones, and resulting spectrum after aliasing and folding is observed, as it would appear in the first Nyquist zone.
It can be observed when signal's frequency is increased in odd Nyquist zones, the signal seems to move from 0 to Fs over 2. But as we increase frequency of signal in even Nyquist zones, the alias signal moves backward from Fs over to 0. Also, for even numbered Nyquist zones, the spectrum will appear in reverse order. And for odd Nyquist zones, it will appear in original order.
Now, let's understand what kind of ADCs can be used for undersampling, and what other things should be kept in mind when choosing the ADC. After sampling rate, the second most important parameter is analog bandwidth of an ADC. Analog input bandwidth is the analog input frequency at which power of the fundamental is reduced by 3 dB with respect to the low frequency value.
TI offers many devices that can do undersampling. One such device is ADC12DJI3200. It is a 12-bit ADC, and can sample up to 6.4 gigasamples per second in single channel mode, and up to 3.2 gigasamples per second in dual channel mode. It has 8 gigahertz of analog input bandwidth, which means it can sample signals in first, second, third, and fourth Nyquist zone.
This concludes our video. Thanks for your time.